Are they? I see nothing in the article about the negative consequences of surprising users with silent failure, for example. Or the fact that it makes little sense in real-world scenarios.
would you object to me defining the piecewise function f:R->R defined to be 1/x for x =/= 0 and 0 for when x=0?
What do you mean by objecting to you defining a function?
That's because the article is purely about the mathematical consistency of using 1 / 0 = 0. It explicitly and repeatedly mentions that it's not about real-world logistics.
> "What do you mean by objecting to you defining a function?"
The author is defining the division function with this special mapping, f, which includes 0 in the domain. Damn near everyone in this thread is confusing that definition with defining the multiplicative inverse, 0⁻.
It's an understandable confusion, but also honestly getting pretty frustrating. That's what he or she is getting at.